Who really flipped the coin?

bobbym · 2009-08-23 02:21:45

Hi

Two students were asked to flip a coin 120 times and record the heads as 1 and the tails as 0 and then hand it in.

Student A handed in:

1100 1011 0110 0100 0110 1010 0110 1001 0101 1011 0011 0111 0100 1001 1010
0110 1001 1010 1100 1110 0101 0100 0101 0101 0101 1001 0010 1100 1001 1011

Student B handed in:

1100 0011 1010 1111 1101 0001 1001 1010 1000 1101 0011 1010 0001 0111 0110
0111 0110 0111 1110 1101 0101 0000 0000 1001 1001 1110 1111 0101 1011 0101

One of them cheated and didn't flip a coin at all. Which one cheated and why?

MathsIsFun · 2009-08-23 09:28:56

Makes a good point!

luca-deltodesco · 2009-08-23 09:48:04

phrontister · 2009-08-23 11:23:13

Last edited by phrontister (2009-08-23 13:02:40)

bobbym · 2009-08-23 21:10:49

Hi phrontister;

None that I am aware of.

Hi MathsisFun and luca-deltodesco;

Correct.

Last edited by bobbym (2009-08-23 22:47:28)

phrontister · 2009-08-24 00:57:15

Hi Bobby,

I doubted that there would be runs such as in your findings and so I conducted my own experiment. Coin tosses were varied...left-handed, right-handed, caught, dropped, high toss, low toss, & some others.

Had to do it while my wife was out, because I'm "spending too much time on that maths forum".

My results:

0110 0110 1100 0011 0101 0111 0101 0111 1101 1011 1010 0001 0011 0000 1011
0101 1000 1111 1001 0010 1101 0001 0011 1101 0001 0101 1111 0111 1000 1011

Well...I'm surprised. It has 3 runs of 5 plus 5 runs of 4.

It also bears out luca's comment:

luca-deltodesco wrote:

And no...I don't think there's a hidden message in my binaries.

I didn't analyse it any further...I just heard the front door open!

Last edited by phrontister (2009-08-24 00:58:50)

bobbym · 2009-08-24 01:13:05

Hi phrontister;

Why the heck didn't you program it! I just did one test on your data and I believe you flipped that coin. I remember doing a blackjack simulation by hand, a long time ago. It was before I got my first computer.

phrontister · 2009-08-24 01:54:23

Hi Bobby,

Why the heck didn't you program it!

I don't know what possessed me! Sometimes I just start writing instead of typing, too!!

But I haven't yet descended to the depths of shop assistants and their utter reliance on calculators, even for the simplest of tasks.

Last edited by phrontister (2009-08-24 01:56:23)

MathsIsFun · 2009-08-24 09:54:14

There is a purity in phrontister's sequence ... no need to worry about pseudorandom issues.

I wonder why noone has thought to include a "random" chip in a standard PC? Just a well-baked transistor would help!

mathsyperson · 2009-08-24 10:28:43

There are some computers that use radioactivity to obtain "truly random" numbers.
Something like drilling a hole in Schrodinger's box and timing how long it takes for the cat to die.

bobbym · 2009-08-24 12:47:22

Hi;

The trouble is flipping a coin is not truly random either, their is a bias to one side because of the uneven weight distribution. Pseudo-random numbers while not truly random, have the statistical properties of randomness.

phrontister · 2009-08-24 13:21:10

Hi Bobby,

bobbym wrote:

The trouble is flipping a coin is not truly random either, their is a bias to one side because of the uneven weight distribution...

I doubt that there was much (any?) influence due to weight-distribution bias in my live experiment. Mixed in with the variations I mentioned above (left-handed, right-handed, caught, dropped, high toss, low toss) were catching-height variations, turning the coin over in my hand varying numbers of times before (and/or after) flipping it and varying the spinning speed. That's all I recall.

I also used varying combinations of those variations: eg, slow spin/high toss; fast spin/low catch/turn over catch.

I never used the same manoeuvre multiple times in a row...and maybe that makes my experiment not truly random.

Last edited by phrontister (2009-08-24 13:38:41)

bobbym · 2009-08-24 13:35:41

Hi phrontister;

I'm not saying the bias developed from the way you tossed the coin but from the fact that a coin is uneven in weight distribution (one side is heavier than the other). When a coin is spun it has a huge bias and when it is flipped:

http://www.codingthewheel.com/archives/ … roposition

Last edited by bobbym (2009-08-24 13:35:55)

phrontister · 2009-08-24 14:26:26

Hi Bobby,

Very interesting article...thanks! Next time there's some coin-flipping to do I'll toss and I'll call!

I hadn't considered the enormous influence that a weight-distribution bias of umpteen vigintillionths of a yoctometer (or any number of vigintillionths of a yoctometer, for that matter) might have on my experiment, otherwise I would have gone to much greater lengths than I did to try to achieve true randomness.

And it's just as well that the author didn't go down to one googolplexth of a yoctometre for the level of perfection in a coin's fabrication, or I might have thought he was just being silly!

bobbym · 2009-08-24 14:31:46

Hi phrontister;

He sounds like a physicist and they are silly, they always worry about the smallest things.

phrontister wrote:

But I haven't yet descended to the depths of shop assistants and their utter reliance on calculators, even for the simplest of tasks.

This is a really interesting and controversial point and deserves it's own thread.

quittyqat · 2009-08-28 07:12:45

MathsIsFun wrote:

There is a purity in phrontister's sequence ... no need to worry about pseudorandom issues.
I wonder why noone has thought to include a "random" chip in a standard PC? Just a well-baked transistor would help!

Noone?

MathsIsFun · 2009-08-28 11:50:40

Whatwaswrongwiththat?

bobbym · 2009-08-28 12:28:04

Hi;

Quittyqat, is the only person in this forum ever to catch me making a similar type error!

phrontister · 2009-08-28 16:15:04

MathsIsFun wrote:

Whatwaswrongwiththat?

"Whatwaswrongwiththat"...a syllabic-alliteration example.

Last edited by phrontister (2009-08-28 16:18:36)

quittyqat · 2009-08-30 07:50:30

quittyqat wrote:

MathsIsFun wrote:
There is a purity in phrontister's sequence ... no need to worry about pseudorandom issues.
I wonder why noone has thought to include a "random" chip in a standard PC? Just a well-baked transistor would help!
Noone?

MathsIsFun wrote:

Whatwaswrongwiththat?

I see... When you wrote that, in your time, it was noon!

phrontister · 2009-08-30 11:33:06

I see... When you wrote that, in your time, it was noon!

"noone"...the forbidden letter gives some nice, extra spice here.

Last edited by phrontister (2009-08-30 21:00:28)

Math Is Fun Forum

#1 2009-08-23 02:21:45

Who really flipped the coin?

#2 2009-08-23 09:28:56

Re: Who really flipped the coin?

#3 2009-08-23 09:48:04

Re: Who really flipped the coin?

#4 2009-08-23 11:23:13

Re: Who really flipped the coin?

#5 2009-08-23 21:10:49

Re: Who really flipped the coin?

#6 2009-08-24 00:57:15

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#7 2009-08-24 01:13:05

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#8 2009-08-24 01:54:23

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#9 2009-08-24 09:54:14

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#10 2009-08-24 10:28:43

Re: Who really flipped the coin?

#11 2009-08-24 12:47:22

Re: Who really flipped the coin?

#12 2009-08-24 13:21:10

Re: Who really flipped the coin?

#13 2009-08-24 13:35:41

Re: Who really flipped the coin?

#14 2009-08-24 14:26:26

Re: Who really flipped the coin?

#15 2009-08-24 14:31:46

Re: Who really flipped the coin?

#16 2009-08-28 07:12:45

Re: Who really flipped the coin?

#17 2009-08-28 11:50:40

Re: Who really flipped the coin?

#18 2009-08-28 12:28:04

Re: Who really flipped the coin?

#19 2009-08-28 16:15:04

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#20 2009-08-30 07:50:30

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#21 2009-08-30 11:33:06

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